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Dicey could perhaps be from Eurydice.

I have no idea the age of these people, but Dicey is the name of the (female) main character of the Tillerman saga of children's books by Cynthia Voigt -- Homecoming, Dicey's Song, etc.c

It's a little hard to comment on most of these without knowing where you found them.

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Squire, Morrisy, Greenup, Elgin, Hynes, Raborn, and Raiford are all probably surnames turned into given names.

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Cyrenus is probably a simplified form of Cyrenius, the name of the governor of Syria in the Gospel of Luke in the King James version of the Bible. Most modern Bible translations use "Quirinius" as the name of the governor in that verse.

Squire is just the English word.
Elgin I'm seeing several possible etymologies if you Google it, ranging from English meaning "noble" to deriving from an Irish name, it's also under user-submitted names here, but not sure how reliable it is. I know it's a place in Illinois, and it's also a place in Scotland.
Gerusha is a variant spelling of Jerusha
Dalt could be short for Dalton.
Rolin could be a medieval diminuative of Roland
Lovina I've seen before, and I think it's a variant of Lavinia
Algie is a nickname for Algernon
Latice is probably a variant spelling of Lettice
Armelda probably comes from Irmhild, like an Anglicization
I swear I've seen Zilphia before, but maybe I'm thinking of Zilpah. They could be related, I guess.